Abstract: Let γ∈(0, 2), let h be the planar Gaussian free field, and consider the γ-Liouville quantum gravity (LQG) metric associated with h. We show that the essential supremum of the Hausdorff dimension of the boundary of a γ-LQG metric ball with respect to the Euclidean (resp. γ-LQG) metric is 2-γdγ2γ+γ2+γ22dγ2 (resp. dγ-1), where dγ is the Hausdorff dimension of the whole plane with respect to the γ-LQG metric. For γ=8/3, in which case d8/3=4, we get that the essential supremum of Euclidean (resp. 8/3-LQG) dimension of a 8/3-LQG ball boundary is 5/4 (resp. 3). We also compute the essential suprema of the Euclidean and γ-LQG Hausdorff dimensions of the intersection of a γ-LQG ball boundary with the set of metric α-thick points of the field h for each α∈R. Our results show that the set of γ/dγ-thick points on the ball boundary has full Euclidean dimension and the set of γ-thick points on the ball boundary has full γ-LQG dimension.